100 results found for "ap fraction-difference nth-term class10" in Class 10.
किसी समान्तर श्रेणी का (9)वां पद (47) और सार्व अंतर (4) है। पहला पद क्या है?
The (9)th term of an AP is (47) and the common difference is (4). What is the first term?
#ap
#first-term
#nth-term
#class10
A (11)
B (13)
C (17)
D (15)
Explanation opens after your attempt
Step 1
Concept
From \(47=a+8\times4\), (a=15). To move from the known term to the first term, subtract (8d).
Step 2
Why this answer is correct
The correct answer is D. (15). From \(47=a+8\times4\), (a=15). To move from the known term to the first term, subtract (8d).
Step 3
Exam Tip
\(47=a+8\times4\) से (a=15)। ज्ञात पद से पहले पद तक जाने के लिए (8d) घटाएं।
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एक समान्तर श्रेणी का (6)वां पद (23) और सार्व अंतर (5) है। पहला पद क्या होगा?
The (6)th term of an AP is (23) and the common difference is (5). What is the first term?
#ap
#first-term
#nth-term
#class10
A (0)
B (3)
C (2)
D (-2)
Explanation opens after your attempt
Step 1
Concept
(23=a+5d=a+25), so (a=-2). When moving backward from a given term, subtract (5d).
Step 2
Why this answer is correct
The correct answer is D. (-2). (23=a+5d=a+25), so (a=-2). When moving backward from a given term, subtract (5d).
Step 3
Exam Tip
(23=a+5d=a+25), इसलिए (a=-2)। दिए गए पद से पीछे जाते समय (5d) घटाया जाता है।
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समान्तर श्रेणी का पहला पद (25) है और (18)वां पद (93) है। सार्व अंतर क्या है?
The first term of an AP is (25) and the (18)th term is (93). What is the common difference?
#ap
#common-difference
#nth-term
#class10
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
From (93=25+17d), (68=17d) so (d=4). For the (18)th term, the multiplier is (17).
Step 2
Why this answer is correct
The correct answer is C. (4). From (93=25+17d), (68=17d) so (d=4). For the (18)th term, the multiplier is (17).
Step 3
Exam Tip
(93=25+17d) से (68=17d) इसलिए (d=4)। (18)वें पद के लिए गुणक (17) होता है।
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एक समान्तर श्रेणी का पहला पद (18) और (16)वां पद (93) है। सार्व अंतर क्या है?
The first term of an AP is (18) and the (16)th term is (93). What is the common difference?
#ap
#common-difference
#nth-term
#class10
A (5)
B (4)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
(93=18+15d), so (75=15d) and (d=5). For the (16)th term, the multiplier is (15).
Step 2
Why this answer is correct
The correct answer is A. (5). (93=18+15d), so (75=15d) and (d=5). For the (16)th term, the multiplier is (15).
Step 3
Exam Tip
(93=18+15d), इसलिए (75=15d) और (d=5)। (16)वें पद के लिए गुणक (15) होगा।
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यदि किसी समान्तर श्रेणी का (10)वां पद (41) और (20)वां पद (81) है, तो उसका सार्व अंतर क्या है?
If the (10)th term of an AP is (41) and the (20)th term is (81), what is its common difference?
#ap
#common-difference
#nth-term
#class10
A (3)
B (5)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(The difference of terms is (81-41=40) and the difference of positions is (10), so (d=4). Use (d=\frac{\)difference of terms}{difference of positions}).
Step 2
Why this answer is correct
\(The correct answer is C. (4). The difference of terms is (81-41=40) and the difference of positions is (10), so (d=4). Use (d=\frac{\)difference of terms}{difference of positions}).
Step 3
Exam Tip
दो पदों का अंतर (81-41=40) है और पद संख्या का अंतर (10), इसलिए (d=4)। \(दो ज्ञात पदों में (d=\frac{\)पदों का अंतर}{स्थान का अंतर}) लगाएं।
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यदि AP का (5)वां पद (27) और (14)वां पद (90) है तो (20)वां पद क्या होगा?
If the (5)th term of an AP is (27) and the (14)th term is (90), what is the (20)th term?
#ap two-terms nth-term class10
A (126)
B (130)
C (132)
D (136)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{90-27}{14-5}=7\) and \(a_{20}=90+6\times7=132\). First find (d) then move forward.
Step 2
Why this answer is correct
The correct answer is C. (132). \(d=\frac{90-27}{14-5}=7\) and \(a_{20}=90+6\times7=132\). First find (d) then move forward.
Step 3
Exam Tip
\(d=\frac{90-27}{14-5}=7\) और \(a_{20}=90+6\times7=132\)। पहले (d) निकालें फिर आगे बढ़ें।
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यदि समान्तर श्रेणी का (4)वां पद (15) और (12)वां पद (55) है तो (16)वां पद क्या होगा?
If the (4)th term of an AP is (15) and the (12)th term is (55), what is the (16)th term?
#ap
#two-terms
#nth-term
#class10
A (70)
B (80)
C (75)
D (85)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{55-15}{12-4}=5\) and \(a_{16}=55+4\times5=75\). First find (d), then the required term.
Step 2
Why this answer is correct
The correct answer is C. (75). \(d=\frac{55-15}{12-4}=5\) and \(a_{16}=55+4\times5=75\). First find (d), then the required term.
Step 3
Exam Tip
\(d=\frac{55-15}{12-4}=5\) और \(a_{16}=55+4\times5=75\)। पहले (d) फिर वांछित पद निकालें।
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यदि AP का (3)वां पद (8) और (8)वां पद (3) है, तो (11)वां पद क्या होगा?
If the (3)rd term of an AP is (8) and the (8)th term is (3), what is the (11)th term?
#ap
#two-terms
#nth-term
#class10
A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{3-8}{8-3}=-1\), so (a_{11}=3+3(-1)=0). Moving from the nearer known term is simple.
Step 2
Why this answer is correct
The correct answer is A. (0). \(d=\frac{3-8}{8-3}=-1\), so (a_{11}=3+3(-1)=0). Moving from the nearer known term is simple.
Step 3
Exam Tip
\(d=\frac{3-8}{8-3}=-1\), इसलिए (a_{11}=3+3(-1)=0)। ज्ञात पास वाले पद से आगे बढ़ना सरल है।
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यदि किसी AP का (p)वां पद (q) और (q)वां पद (p) है, तो उसका ((p+q))वां पद क्या होगा?
If the (p)th term of an AP is (q) and the (q)th term is (p), what is its ((p+q))th term?
#ap
#symbolic
#nth-term
#class10
A (0)
B (p+q)
C (p-q)
D (q-p)
Explanation opens after your attempt
Step 1
Concept
Subtracting the relations gives (d=-1), and substitution gives \(a_{p+q}=0\). Even in symbolic APs, use (a_n=a+(n-1)d).
Step 2
Why this answer is correct
The correct answer is A. (0). Subtracting the relations gives (d=-1), and substitution gives \(a_{p+q}=0\). Even in symbolic APs, use (a_n=a+(n-1)d).
Step 3
Exam Tip
संबंधों को घटाने पर (d=-1) और आगे रखने पर \(a_{p+q}=0\) मिलता है। प्रतीकात्मक AP में भी (a_n=a+(n-1)d) ही लगाएं।
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यदि किसी समान्तर श्रेणी का (5)वां पद (16) और (9)वां पद (32) है, तो (13)वां पद क्या होगा?
If the (5)th term of an AP is (16) and the (9)th term is (32), what is the (13)th term?
#ap
#two-known-terms
#nth-term
#class10
A (44)
B (46)
C (48)
D (50)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{32-16}{9-5}=4\), so \(a_{13}=32+4\times4=48\). Equal position gaps give equal term gaps in an AP.
Step 2
Why this answer is correct
The correct answer is C. (48). \(d=\frac{32-16}{9-5}=4\), so \(a_{13}=32+4\times4=48\). Equal position gaps give equal term gaps in an AP.
Step 3
Exam Tip
\(d=\frac{32-16}{9-5}=4\), इसलिए \(a_{13}=32+4\times4=48\)। समान स्थान अंतर होने पर पदों का अंतर भी समान होता है।
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यदि किसी समान्तर श्रेणी का पहला पद (7) और सार्व अंतर (4) है, तो उसका (18)वां पद क्या होगा?
If the first term of an AP is (7) and the common difference is (4), what is its (18)th term?
#ap
#nth-term
#medium
#class10
A (75)
B (71)
C (79)
D (83)
Explanation opens after your attempt
Step 1
Concept
Using (a_n=a+(n-1)d), \(7+17\times4=75\). Exam tip: do not forget (n-1).
Step 2
Why this answer is correct
The correct answer is A. (75). Using (a_n=a+(n-1)d), \(7+17\times4=75\). Exam tip: do not forget (n-1).
Step 3
Exam Tip
सूत्र (a_n=a+(n-1)d) लगाने पर \(7+17\times4=75\)। परीक्षा में (n-1) को भूलना नहीं चाहिए।
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यदि एपी का प्रथम पद (-12) और सार्व अंतर (5) है तो (16)वाँ पद क्या होगा?
If the first term of an AP is (-12) and the common difference is (5), what is the (16)th term?
#ap
#nth-term
#easy
#class10
A (61)
B (63)
C (65)
D (67)
Explanation opens after your attempt
Step 1
Concept
\(a_{16}=-12+15\times5=63\). First calculate (15d), then add the first term.
Step 2
Why this answer is correct
The correct answer is B. (63). \(a_{16}=-12+15\times5=63\). First calculate (15d), then add the first term.
Step 3
Exam Tip
\(a_{16}=-12+15\times5=63\)। पहले (15d) निकालें फिर प्रथम पद जोड़ें।
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यदि किसी एपी का प्रथम पद (9) और सार्व अंतर (10) है तो (7)वाँ पद क्या होगा?
If the first term of an AP is (9) and the common difference is (10), what is the (7)th term?
#ap
#nth-term
#easy
#class10
A (59)
B (69)
C (79)
D (89)
Explanation opens after your attempt
Step 1
Concept
\(a_7=9+6\times10=69\). For the (7)th term, (6d) is added.
Step 2
Why this answer is correct
The correct answer is B. (69). \(a_7=9+6\times10=69\). For the (7)th term, (6d) is added.
Step 3
Exam Tip
\(a_7=9+6\times10=69\)। (7)वें पद के लिए (6d) जोड़ना होता है।
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यदि एपी का प्रथम पद (-2) और सार्व अंतर (6) है तो (12)वाँ पद क्या होगा?
If the first term of an AP is (-2) and the common difference is (6), what is the (12)th term?
#ap
#nth-term
#easy
#class10
A (62)
B (64)
C (66)
D (68)
Explanation opens after your attempt
Step 1
Concept
\(a_{12}=-2+11\times6=64\). Multiply first and then add (-2).
Step 2
Why this answer is correct
The correct answer is B. (64). \(a_{12}=-2+11\times6=64\). Multiply first and then add (-2).
Step 3
Exam Tip
\(a_{12}=-2+11\times6=64\)। पहले गुणा करें फिर (-2) जोड़ें।
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यदि एपी का प्रथम पद (15) और सार्व अंतर (-4) है तो (8)वाँ पद क्या होगा?
If the first term of an AP is (15) and the common difference is (-4), what is the (8)th term?
#ap
#nth-term
#easy
#class10
A (-13)
B (-11)
C (-9)
D (-7)
Explanation opens after your attempt
Step 1
Concept
(a_8=15+7(-4)=-13). Writing negative (d) in brackets is useful.
Step 2
Why this answer is correct
The correct answer is A. (-13). (a_8=15+7(-4)=-13). Writing negative (d) in brackets is useful.
Step 3
Exam Tip
(a_8=15+7(-4)=-13)। ऋणात्मक (d) को कोष्ठक में लिखना उपयोगी है।
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यदि किसी एपी का प्रथम पद (5) और सार्व अंतर (3) है तो (8)वाँ पद क्या होगा?
If the first term of an AP is (5) and common difference is (3), what is the (8)th term?
#ap
#nth-term
#easy
#class10
A (23)
B (24)
C (26)
D (28)
Explanation opens after your attempt
Step 1
Concept
Using (a_n=a+(n-1)d), \(5+7\times3=26\). In exams, do not forget (n-1).
Step 2
Why this answer is correct
The correct answer is C. (26). Using (a_n=a+(n-1)d), \(5+7\times3=26\). In exams, do not forget (n-1).
Step 3
Exam Tip
सूत्र (a_n=a+(n-1)d) लगाएं तो \(5+7\times3=26\)। परीक्षा में (n-1) लेना न भूलें।
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यदि समांतर श्रेढ़ी का प्रथम पद (6) और सार्व अंतर (7) है, तो (11)वाँ पद क्या है?
If the first term of an AP is (6) and the common difference is (7), what is the (11)th term?
#ap common difference
#nth term
#easy
A (83)
B (70)
C (79)
D (76)
Explanation opens after your attempt
Step 1
Concept
\(a_{11}=6+10\times7=76\). Up to the (11)th term, the difference is added (10) times.
Step 2
Why this answer is correct
The correct answer is D. (76). \(a_{11}=6+10\times7=76\). Up to the (11)th term, the difference is added (10) times.
Step 3
Exam Tip
\(a_{11}=6+10\times7=76\)। (11)वें पद तक (10) बार अंतर जुड़ता है।
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किसी समान्तर श्रेणी का (12)वां पद (71) और सार्व अंतर (5) है। पहला पद क्या होगा?
The (12)th term of an AP is (71) and the common difference is (5). What is the first term?
#ap first-term known-term class10
A (18)
B (14)
C (20)
D (16)
Explanation opens after your attempt
Step 1
Concept
From \(71=a+11\times5\), (a=16). To move from the known term to the first term subtract (11d).
Step 2
Why this answer is correct
The correct answer is D. (16). From \(71=a+11\times5\), (a=16). To move from the known term to the first term subtract (11d).
Step 3
Exam Tip
\(71=a+11\times5\) से (a=16)। ज्ञात पद से पहले पद तक जाने के लिए (11d) घटाएं।
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यदि AP का पहला पद (22) और \(a_{32}=177\) है तो सार्व अंतर क्या होगा?
If the first term of an AP is (22) and \(a_{32}=177\), what is the common difference?
#ap common-difference nth-term class10
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
From (177=22+31d), (155=31d) and (d=5). In the (32)nd term (31d) is added.
Step 2
Why this answer is correct
The correct answer is C. (5). From (177=22+31d), (155=31d) and (d=5). In the (32)nd term (31d) is added.
Step 3
Exam Tip
(177=22+31d) से (155=31d) और (d=5)। (32)वें पद में (31d) जुड़ता है।
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किसी AP का पहला पद (31) है और \(a_{19}=139\) है। सार्व अंतर क्या है?
The first term of an AP is (31) and \(a_{19}=139\). What is the common difference?
#ap common-difference nth-term class10
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
From (139=31+18d), (108=18d) so (d=6). For the (19)th term (18d) is added.
Step 2
Why this answer is correct
The correct answer is C. (6). From (139=31+18d), (108=18d) so (d=6). For the (19)th term (18d) is added.
Step 3
Exam Tip
(139=31+18d) से (108=18d) इसलिए (d=6)। (19)वें पद के लिए (18d) जुड़ता है।
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एक समांतर श्रेढ़ी का प्रथम पद (25) और सार्व अंतर (4) है। (21)वाँ पद क्या होगा?
The first term of an AP is (25) and the common difference is (4). What will be the (21)st term?
#ap formula
#nth term
#class 10
A (101)
B (105)
C (109)
D (96)
Explanation opens after your attempt
Step 1
Concept
\(a_{21}=25+20\times4=105\). Do not forget to subtract (1) from the term number.
Step 2
Why this answer is correct
The correct answer is B. (105). \(a_{21}=25+20\times4=105\). Do not forget to subtract (1) from the term number.
Step 3
Exam Tip
\(a_{21}=25+20\times4=105\)। पद संख्या से (1) घटाना न भूलें।
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समांतर श्रेढ़ी में प्रथम पद (a=4) और सार्व अंतर (d=3) है। इसका (10)वाँ पद क्या होगा?
In an AP, first term (a=4) and common difference (d=3). What is the (10)th term?
#arithmetic progression
#nth term
#easy
#class 10
A (31)
B (30)
C (34)
D (27)
Explanation opens after your attempt
Step 1
Concept
Using (a_n=a+(n-1)d), \(a_{10}=4+9\times3=31\). Exam tip: write (n-1) carefully.
Step 2
Why this answer is correct
The correct answer is A. (31). Using (a_n=a+(n-1)d), \(a_{10}=4+9\times3=31\). Exam tip: write (n-1) carefully.
Step 3
Exam Tip
सूत्र (a_n=a+(n-1)d) लगाने पर \(a_{10}=4+9\times3=31\)। परीक्षा में (n-1) को ध्यान से लिखें।
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समान्तर श्रेणी \(23,31,39,\ldots\) के (n)वें पद का सूत्र \(a_n=8n+15\) है। (36)वां पद क्या होगा?
The (n)th-term formula of the AP \(23,31,39,\ldots\) is \(a_n=8n+15\). What is the (36)th term?
#ap direct-formula nth-term class10
A (293)
B (301)
C (303)
D (311)
Explanation opens after your attempt
Step 1
Concept
\(a_{36}=8\times36+15=303\). Put (n=36) in the formed formula to get the answer directly.
Step 2
Why this answer is correct
The correct answer is C. (303). \(a_{36}=8\times36+15=303\). Put (n=36) in the formed formula to get the answer directly.
Step 3
Exam Tip
\(a_{36}=8\times36+15=303\)। बने हुए सूत्र में (n=36) रखकर सीधे उत्तर पाएं।
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यदि किसी AP का (r)वां पद (3r-2) और (d=4) है तो ((r+6))वां पद क्या होगा?
If the (r)th term of an AP is (3r-2) and (d=4), what is the ((r+6))th term?
#ap symbolic nth-term class10
A (3r+18)
B (3r+20)
C (3r+22)
D (3r+24)
Explanation opens after your attempt
Correct Answer
C. (3r+22)
Step 1
Concept
The ((r+6))th term is (6d) ahead of the (r)th term so (3r-2+24=3r+22). In symbolic questions look at the position gap.
Step 2
Why this answer is correct
The correct answer is C. (3r+22). The ((r+6))th term is (6d) ahead of the (r)th term so (3r-2+24=3r+22). In symbolic questions look at the position gap.
Step 3
Exam Tip
((r+6))वां पद (r)वें पद से (6d) आगे है इसलिए (3r-2+24=3r+22)। प्रतीकात्मक प्रश्न में स्थान अंतर देखें।
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समान्तर श्रेणी \(19,26,33,\ldots\) के (n)वें पद का सूत्र \(a_n=7n+12\) है। (41)वां पद क्या होगा?
The (n)th-term formula of the AP \(19,26,33,\ldots\) is \(a_n=7n+12\). What is the (41)st term?
#ap
#direct-formula
#nth-term
#class10
A (294)
B (304)
C (309)
D (299)
Explanation opens after your attempt
Step 1
Concept
\(a_{41}=7\times41+12=299\). Put only (n=41) in the formed formula.
Step 2
Why this answer is correct
The correct answer is D. (299). \(a_{41}=7\times41+12=299\). Put only (n=41) in the formed formula.
Step 3
Exam Tip
\(a_{41}=7\times41+12=299\)। बने हुए सूत्र में केवल (n=41) रखें।
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यदि किसी समान्तर श्रेणी का (m)वां पद (2m+3) और (d=2) है तो ((m+5))वां पद क्या होगा?
If the (m)th term of an AP is (2m+3) and (d=2), what is the ((m+5))th term?
#ap
#symbolic
#nth-term
#class10
A (2m+8)
B (2m+10)
C (2m+11)
D (2m+13)
Explanation opens after your attempt
Correct Answer
D. (2m+13)
Step 1
Concept
The ((m+5))th term is (5d) ahead of the (m)th term, so (2m+3+10=2m+13). In symbolic terms, look at the position gap.
Step 2
Why this answer is correct
The correct answer is D. (2m+13). The ((m+5))th term is (5d) ahead of the (m)th term, so (2m+3+10=2m+13). In symbolic terms, look at the position gap.
Step 3
Exam Tip
((m+5))वां पद (m)वें पद से (5d) आगे है इसलिए (2m+3+10=2m+13)। प्रतीकात्मक पदों में भी स्थान अंतर देखें।
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समान्तर श्रेणी \(11,17,23,\ldots\) का (n)वां पद \(a_n=6n+5\) है। इसका (32)वां पद क्या होगा?
The (n)th term of the AP \(11,17,23,\ldots\) is \(a_n=6n+5\). What is its (32)nd term?
#ap
#direct-formula
#nth-term
#class10
A (191)
B (197)
C (203)
D (209)
Explanation opens after your attempt
Step 1
Concept
\(a_{32}=6\times32+5=197\). Substitute the correct value of (n) in the formed formula.
Step 2
Why this answer is correct
The correct answer is B. (197). \(a_{32}=6\times32+5=197\). Substitute the correct value of (n) in the formed formula.
Step 3
Exam Tip
\(a_{32}=6\times32+5=197\)। बनाए गए सूत्र में (n) का सही मान रखें।
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यदि एपी का (4)था पद (21) और (d=6) है तो (10)वाँ पद क्या होगा?
If the (4)th term of an AP is (21) and (d=6), what is the (10)th term?
#ap
#nth-term
#easy
#class10
A (53)
B (55)
C (57)
D (59)
Explanation opens after your attempt
Step 1
Concept
The (10)th term is (6d) after the (4)th term, so (21+36=57). Use the difference in term numbers directly.
Step 2
Why this answer is correct
The correct answer is C. (57). The (10)th term is (6d) after the (4)th term, so (21+36=57). Use the difference in term numbers directly.
Step 3
Exam Tip
(10)वाँ पद (4)थे पद से (6d) आगे है इसलिए (21+36=57)। पद संख्या का अंतर सीधे उपयोग करें।
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यदि किसी एपी का (3)रा पद (14) और (d=5) है तो (7)वाँ पद क्या होगा?
If the (3)rd term of an AP is (14) and (d=5), what is the (7)th term?
#ap
#nth-term
#easy
#class10
A (29)
B (31)
C (34)
D (36)
Explanation opens after your attempt
Step 1
Concept
The (7)th term is (4d) after the (3)rd term, so (14+20=34). Count the gap between terms correctly.
Step 2
Why this answer is correct
The correct answer is C. (34). The (7)th term is (4d) after the (3)rd term, so (14+20=34). Count the gap between terms correctly.
Step 3
Exam Tip
(7)वाँ पद (3)रे पद से (4d) आगे है इसलिए (14+20=34)। बीच के पदों की संख्या सही गिनें।
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यदि किसी एपी का (5)वाँ पद (22) और (d=6) है तो (8)वाँ पद क्या है?
If the (5)th term of an AP is (22) and (d=6), what is the (8)th term?
#ap
#nth-term
#easy
#class10
A (34)
B (36)
C (38)
D (40)
Explanation opens after your attempt
Step 1
Concept
The (8)th term is (3d) after the (5)th term, so (22+18=40). Counting the gap between terms is an easy method.
Step 2
Why this answer is correct
The correct answer is D. (40). The (8)th term is (3d) after the (5)th term, so (22+18=40). Counting the gap between terms is an easy method.
Step 3
Exam Tip
(8)वाँ पद (5)वें पद से (3d) आगे है इसलिए (22+18=40)। पदों का अंतर गिनना आसान तरीका है।
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यदि एपी का (7)वाँ पद (31) है और (d=4) है तो (10)वाँ पद क्या होगा?
If the (7)th term of an AP is (31) and (d=4), what is the (10)th term?
#ap
#nth-term
#easy
#class10
A (39)
B (41)
C (43)
D (45)
Explanation opens after your attempt
Step 1
Concept
The (10)th term is (3d) after the (7)th term, so \(31+3\times4=43\). The difference method is quick for nearby terms.
Step 2
Why this answer is correct
The correct answer is C. (43). The (10)th term is (3d) after the (7)th term, so \(31+3\times4=43\). The difference method is quick for nearby terms.
Step 3
Exam Tip
(10)वाँ पद (7)वें पद से (3d) आगे है इसलिए \(31+3\times4=43\)। पास के पदों के लिए अंतर विधि तेज होती है।
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समान्तर श्रेणी \(\frac{2}{3},\frac{4}{3},2,\ldots\) का (28)वां पद क्या है?
What is the (28)th term of the AP \(\frac{2}{3},\frac{4}{3},2,\ldots\)?
#ap fraction-ap nth-term class10
A (18)
B \(\frac{56}{3}\)
C (19)
D \(\frac{58}{3}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{56}{3}\)
Step 1
Concept
Here \(a=\frac{2}{3}\) and \(d=\frac{2}{3}\) so \(a_{28}=\frac{2}{3}+27\cdot\frac{2}{3}=\frac{56}{3}\). Simplify multiplication first in fractions.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{56}{3}\). Here \(a=\frac{2}{3}\) and \(d=\frac{2}{3}\) so \(a_{28}=\frac{2}{3}+27\cdot\frac{2}{3}=\frac{56}{3}\). Simplify multiplication first in fractions.
Step 3
Exam Tip
यहां \(a=\frac{2}{3}\) और \(d=\frac{2}{3}\) है इसलिए \(a_{28}=\frac{2}{3}+27\cdot\frac{2}{3}=\frac{56}{3}\)। भिन्नों में गुणन को पहले सरल करें।
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समान्तर श्रेणी \(\frac{3}{4},\frac{5}{4},\frac{7}{4},\ldots\) का (31)वां पद क्या है?
What is the (31)st term of the AP \(\frac{3}{4},\frac{5}{4},\frac{7}{4},\ldots\)?
#ap
#fraction-ap
#nth-term
#class10
A \(\frac{61}{4}\)
B \(\frac{63}{4}\)
C \(\frac{65}{4}\)
D \(\frac{67}{4}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{63}{4}\)
Step 1
Concept
Here \(a=\frac{3}{4}\) and \(d=\frac{1}{2}\) so \(a_{31}=\frac{3}{4}+30\cdot\frac{1}{2}=\frac{63}{4}\). Use a common denominator for fractions.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{63}{4}\). Here \(a=\frac{3}{4}\) and \(d=\frac{1}{2}\) so \(a_{31}=\frac{3}{4}+30\cdot\frac{1}{2}=\frac{63}{4}\). Use a common denominator for fractions.
Step 3
Exam Tip
यहां \(a=\frac{3}{4}\) और \(d=\frac{1}{2}\) है इसलिए \(a_{31}=\frac{3}{4}+30\cdot\frac{1}{2}=\frac{63}{4}\)। भिन्नों में समान हर बनाएं।
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समान्तर श्रेणी \(\frac{1}{2},1,\frac{3}{2},\ldots\) का (40)वां पद क्या है?
What is the (40)th term of the AP \(\frac{1}{2},1,\frac{3}{2},\ldots\)?
#ap
#fraction-ap
#nth-term
#class10
A (19)
B (19.5)
C (20)
D (20.5)
Explanation opens after your attempt
Step 1
Concept
Here \(a=\frac{1}{2}\), \(d=\frac{1}{2}\), so \(a_{40}=\frac{1}{2}+39\cdot\frac{1}{2}=20\). Fractions can also be checked as decimals.
Step 2
Why this answer is correct
The correct answer is C. (20). Here \(a=\frac{1}{2}\), \(d=\frac{1}{2}\), so \(a_{40}=\frac{1}{2}+39\cdot\frac{1}{2}=20\). Fractions can also be checked as decimals.
Step 3
Exam Tip
यहां \(a=\frac{1}{2}\), \(d=\frac{1}{2}\), इसलिए \(a_{40}=\frac{1}{2}+39\cdot\frac{1}{2}=20\)। भिन्नों को दशमलव में बदलकर भी जांच सकते हैं।
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समांतर श्रेढ़ी का सामान्य पद \(a_n=7n+2\) है। (11)वाँ पद ज्ञात कीजिए।
The general term of an AP is \(a_n=7n+2\). Find the (11)th term.
#ap
#general term
#nth term
A (72)
B (84)
C (79)
D (77)
Explanation opens after your attempt
Step 1
Concept
\(a_{11}=7\times11+2=79\). The main step is substituting the correct term number in the general term.
Step 2
Why this answer is correct
The correct answer is C. (79). \(a_{11}=7\times11+2=79\). The main step is substituting the correct term number in the general term.
Step 3
Exam Tip
\(a_{11}=7\times11+2=79\)। सामान्य पद में सही पद संख्या रखना ही मुख्य कदम है।
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यदि हर अगला पद पिछले पद से (9) अधिक है, तो सार्व अंतर क्या है?
If every next term is (9) more than the previous term, what is the common difference?
#arithmetic-progression
#common-difference
#class10
A (0)
B (1)
C (9)
D (-9)
Explanation opens after your attempt
Step 1
Concept
Being (9) more each time means (d=9). This is the identity of an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is C. (9). Being (9) more each time means (d=9). This is the identity of an arithmetic progression.
Step 3
Exam Tip
हर बार (9) अधिक होने का अर्थ (d=9) है। यही समांतर श्रेढ़ी की पहचान है।
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यदि AP \(z,z+5,z+10,\ldots\) का (19)वां पद (112) है तो (z) क्या होगा?
If the (19)th term of the AP \(z,z+5,z+10,\ldots\) is (112), what is (z)?
#ap variable-first-term nth-term class10
A (18)
B (20)
C (22)
D (24)
Explanation opens after your attempt
Step 1
Concept
From \(112=z+18\times5\), (z=22). Treat the variable first term as (a) and apply the formula.
Step 2
Why this answer is correct
The correct answer is C. (22). From \(112=z+18\times5\), (z=22). Treat the variable first term as (a) and apply the formula.
Step 3
Exam Tip
\(112=z+18\times5\) से (z=22)। चर वाले पहले पद को (a) मानकर सूत्र लगाएं।
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समान्तर श्रेणी \(7,12,17,\ldots\) में (180) से कम अंतिम पद क्या है?
In the AP \(7,12,17,\ldots\), what is the last term less than (180)?
#ap last-term-less-than nth-term class10
A (172)
B (175)
C (177)
D (179)
Explanation opens after your attempt
Step 1
Concept
The terms are (7+5(n-1)). The last term less than (180) is (177) because the next term will be (182).
Step 2
Why this answer is correct
The correct answer is C. (177). The terms are (7+5(n-1)). The last term less than (180) is (177) because the next term will be (182).
Step 3
Exam Tip
पद (7+5(n-1)) हैं। (180) से कम अंतिम पद (177) है क्योंकि अगला पद (182) होगा।
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समान्तर श्रेणी \(105,98,91,\ldots\) का प्रथम ऋणात्मक पद कौन-सा है?
Which is the first negative term of the AP \(105,98,91,\ldots\)?
#ap first-negative-term nth-term class10
A (15)वां / (15)th
B (16)वां / (16)th
C (17)वां / (17)th
D (18)वां / (18)th
Explanation opens after your attempt
Correct Answer
C. (17)वां / (17)th
Step 1
Concept
(a_n=105+(n-1)(-7)=112-7n). From \(a_n<0\), (n>16) so the first negative term is the (17)th.
Step 2
Why this answer is correct
The correct answer is C. (17)वां / (17)th. (a_n=105+(n-1)(-7)=112-7n). From \(a_n<0\), (n>16) so the first negative term is the (17)th.
Step 3
Exam Tip
(a_n=105+(n-1)(-7)=112-7n)। \(a_n<0\) से (n>16) इसलिए पहला ऋणात्मक पद (17)वां है।
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समान्तर श्रेणी \(26,35,44,\ldots\) का कौन-सा पद (206) है?
Which term of the AP \(26,35,44,\ldots\) is (206)?
#ap term-number nth-term class10
A (19)वां / (19)th
B (20)वां / (20)th
C (21)वां / (21)st
D (22)वां / (22)nd
Explanation opens after your attempt
Correct Answer
C. (21)वां / (21)st
Step 1
Concept
From (206=26+(n-1)9), (180=9(n-1)) so (n=21). Divide the difference between the term and first term by (d).
Step 2
Why this answer is correct
The correct answer is C. (21)वां / (21)st. From (206=26+(n-1)9), (180=9(n-1)) so (n=21). Divide the difference between the term and first term by (d).
Step 3
Exam Tip
(206=26+(n-1)9) से (180=9(n-1)) इसलिए (n=21)। पद और पहले पद का अंतर (d) से भाग दें।
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समान्तर श्रेणी \(9,17,25,\ldots\) का कौन-सा पद (201) है?
Which term of the AP \(9,17,25,\ldots\) is (201)?
#ap term-position nth-term class10
A (23)वां / (23)rd
B (24)वां / (24)th
C (25)वां / (25)th
D (26)वां / (26)th
Explanation opens after your attempt
Correct Answer
C. (25)वां / (25)th
Step 1
Concept
From (201=9+(n-1)8), (192=8(n-1)) and (n=25). If the term number is an integer the answer is on the right track.
Step 2
Why this answer is correct
The correct answer is C. (25)वां / (25)th. From (201=9+(n-1)8), (192=8(n-1)) and (n=25). If the term number is an integer the answer is on the right track.
Step 3
Exam Tip
(201=9+(n-1)8) से (192=8(n-1)) और (n=25)। पद संख्या पूर्णांक आए तो उत्तर सही दिशा में है।
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यदि समान्तर श्रेणी \(y,y+6,y+12,\ldots\) का (12)वां पद (89) है तो (y) का मान क्या है?
If the (12)th term of the AP \(y,y+6,y+12,\ldots\) is (89), what is the value of (y)?
#ap
#variable-first-term
#nth-term
#class10
A (17)
B (19)
C (21)
D (23)
Explanation opens after your attempt
Step 1
Concept
From \(89=y+11\times6\), (y=23). Treat the variable first term directly as (a).
Step 2
Why this answer is correct
The correct answer is D. (23). From \(89=y+11\times6\), (y=23). Treat the variable first term directly as (a).
Step 3
Exam Tip
\(89=y+11\times6\) से (y=23)। चर वाले पहले पद को सीधे (a) मानें।
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समान्तर श्रेणी \(2,6,10,\ldots\) में (75) से कम अंतिम पद क्या है?
In the AP \(2,6,10,\ldots\), what is the last term less than (75)?
#ap
#last-term-less-than
#nth-term
#class10
A (74)
B (70)
C (72)
D (76)
Explanation opens after your attempt
Step 1
Concept
The terms of this sequence are (2+4(n-1)). The last term less than (75) is (74).
Step 2
Why this answer is correct
The correct answer is A. (74). The terms of this sequence are (2+4(n-1)). The last term less than (75) is (74).
Step 3
Exam Tip
इस श्रेणी के पद (2+4(n-1)) हैं। (75) से कम अंतिम पद (74) है।
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समान्तर श्रेणी \(72,66,60,\ldots\) का प्रथम ऋणात्मक पद कौन-सा है?
Which is the first negative term of the AP \(72,66,60,\ldots\)?
#ap
#first-negative-term
#nth-term
#class10
A (13)वां / (13)th
B (14)वां / (14)th
C (15)वां / (15)th
D (16)वां / (16)th
Explanation opens after your attempt
Correct Answer
B. (14)वां / (14)th
Step 1
Concept
(a_n=72+(n-1)(-6)=78-6n). From \(a_n<0\), (n>13) so the first negative term is the (14)th.
Step 2
Why this answer is correct
The correct answer is B. (14)वां / (14)th. (a_n=72+(n-1)(-6)=78-6n). From \(a_n<0\), (n>13) so the first negative term is the (14)th.
Step 3
Exam Tip
(a_n=72+(n-1)(-6)=78-6n)। \(a_n<0\) से (n>13) इसलिए पहला ऋणात्मक पद (14)वां है।
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समान्तर श्रेणी \(14,23,32,\ldots\) का कौन-सा पद (185) है?
Which term of the AP \(14,23,32,\ldots\) is (185)?
#ap
#term-number
#nth-term
#class10
A (18)वां / (18)th
B (19)वां / (19)th
C (20)वां / (20)th
D (21)वां / (21)th
Explanation opens after your attempt
Correct Answer
C. (20)वां / (20)th
Step 1
Concept
From (185=14+(n-1)9), (171=9(n-1)) and (n=20). Divide the difference by (d) to get the term number.
Step 2
Why this answer is correct
The correct answer is C. (20)वां / (20)th. From (185=14+(n-1)9), (171=9(n-1)) and (n=20). Divide the difference by (d) to get the term number.
Step 3
Exam Tip
(185=14+(n-1)9) से (171=9(n-1)) और (n=20)। अंतर को (d) से भाग देकर पद संख्या पाएं।
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समान्तर श्रेणी \(21,29,37,\ldots\) का कौन-सा पद (149) है?
Which term of the AP \(21,29,37,\ldots\) is (149)?
#ap
#term-position
#nth-term
#class10
A (15)वां / (15)th
B (16)वां / (16)th
C (17)वां / (17)th
D (18)वां / (18)th
Explanation opens after your attempt
Correct Answer
C. (17)वां / (17)th
Step 1
Concept
From (149=21+(n-1)8), (128=8(n-1)) so (n=17). When term number is asked, treat the given term as \(a_n\).
Step 2
Why this answer is correct
The correct answer is C. (17)वां / (17)th. From (149=21+(n-1)8), (128=8(n-1)) so (n=17). When term number is asked, treat the given term as \(a_n\).
Step 3
Exam Tip
(149=21+(n-1)8) से (128=8(n-1)) इसलिए (n=17)। पद संख्या पूछी हो तो दिए पद को \(a_n\) मानें।
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यदि समान्तर श्रेणी \(x, x+4, x+8,\ldots\) का (10)वां पद (50) है, तो (x) का मान क्या है?
If the (10)th term of the AP \(x, x+4, x+8,\ldots\) is (50), what is the value of (x)?
#ap
#variable-first-term
#nth-term
#class10
A (10)
B (12)
C (14)
D (16)
Explanation opens after your attempt
Step 1
Concept
\(50=x+9\times4\), so (x=14). Treat the variable first term as (a) and apply the formula.
Step 2
Why this answer is correct
The correct answer is C. (14). \(50=x+9\times4\), so (x=14). Treat the variable first term as (a) and apply the formula.
Step 3
Exam Tip
\(50=x+9\times4\), इसलिए (x=14)। चर वाले पहले पद को (a) मानकर सूत्र लगाएं।
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एक समान्तर श्रेणी में (a=30) और (d=-2) है। कौन-सा पद (0) होगा?
In an AP, (a=30) and (d=-2). Which term will be (0)?
#ap
#zero-term
#nth-term
#class10
A (14)वां / (14)th
B (15)वां / (15)th
C (16)वां / (16)th
D (17)वां / (17)th
Explanation opens after your attempt
Correct Answer
C. (16)वां / (16)th
Step 1
Concept
From (0=30+(n-1)(-2)), (2(n-1)=30), so (n=16). Use the same nth-term formula even for the zero term.
Step 2
Why this answer is correct
The correct answer is C. (16)वां / (16)th. From (0=30+(n-1)(-2)), (2(n-1)=30), so (n=16). Use the same nth-term formula even for the zero term.
Step 3
Exam Tip
(0=30+(n-1)(-2)) से (2(n-1)=30), अतः (n=16)। शून्य पद के लिए भी वही (n)वां पद सूत्र लगाएं।
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समान्तर श्रेणी \(45,40,35,\ldots\) का प्रथम ऋणात्मक पद कौन-सा है?
Which is the first negative term of the AP \(45,40,35,\ldots\)?
#ap
#first-negative-term
#nth-term
#class10
A (10)वां / (10)th
B (11)वां / (11)th
C (12)वां / (12)th
D (13)वां / (13)th
Explanation opens after your attempt
Correct Answer
B. (11)वां / (11)th
Step 1
Concept
(a_n=45+(n-1)(-5)=50-5n). From \(a_n<0\), (n>10), so the first negative term is the (11)th.
Step 2
Why this answer is correct
The correct answer is B. (11)वां / (11)th. (a_n=45+(n-1)(-5)=50-5n). From \(a_n<0\), (n>10), so the first negative term is the (11)th.
Step 3
Exam Tip
(a_n=45+(n-1)(-5)=50-5n)। \(a_n<0\) से (n>10), इसलिए पहला ऋणात्मक पद (11)वां है।
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समान्तर श्रेणी \(15,21,27,\ldots\) का कौन-सा पद (111) है?
Which term of the AP \(15,21,27,\ldots\) is (111)?
#ap
#term-number
#nth-term
#class10
A (15)वां / (15)th
B (16)वां / (16)th
C (17)वां / (17)th
D (18)वां / (18)th
Explanation opens after your attempt
Correct Answer
C. (17)वां / (17)th
Step 1
Concept
(111=15+(n-1)6), so (96=6(n-1)) and (n=17). For term number, divide the difference by (d).
Step 2
Why this answer is correct
The correct answer is C. (17)वां / (17)th. (111=15+(n-1)6), so (96=6(n-1)) and (n=17). For term number, divide the difference by (d).
Step 3
Exam Tip
(111=15+(n-1)6), इसलिए (96=6(n-1)) और (n=17)। पद संख्या में अंतर को (d) से भाग दें।
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किसी समान्तर श्रेणी का (8)वां पद (35) और (d=4) है। \(a_1\) क्या होगा?
The (8)th term of an AP is (35) and (d=4). What is \(a_1\)?
#ap
#first-term
#nth-term
#class10
A (11)
B (9)
C (7)
D (13)
Explanation opens after your attempt
Step 1
Concept
\(35=a+7\times4\), so (a=7). For the (8)th term, subtract (7d).
Step 2
Why this answer is correct
The correct answer is C. (7). \(35=a+7\times4\), so (a=7). For the (8)th term, subtract (7d).
Step 3
Exam Tip
\(35=a+7\times4\), इसलिए (a=7)। (8)वें पद के लिए (7d) घटाएं।
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समान्तर श्रेणी \(3,8,13,\ldots\) का कौन-सा पद (88) है?
Which term of the AP \(3,8,13,\ldots\) is (88)?
#ap
#term-position
#nth-term
#class10
A (18)वां / (18)th
B (17)वां / (17)th
C (16)वां / (16)th
D (19)वां / (19)th
Explanation opens after your attempt
Correct Answer
A. (18)वां / (18)th
Step 1
Concept
From (88=3+(n-1)5), (85=5(n-1)), hence (n=18). In term-number questions, treat the given term as \(a_n\).
Step 2
Why this answer is correct
The correct answer is A. (18)वां / (18)th. From (88=3+(n-1)5), (85=5(n-1)), hence (n=18). In term-number questions, treat the given term as \(a_n\).
Step 3
Exam Tip
(88=3+(n-1)5) से (85=5(n-1)), अतः (n=18)। पद संख्या के प्रश्न में दिए पद को \(a_n\) मानें।
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यदि समान्तर श्रेणी का पहला पद (16) और \(a_{26}=116\) है तो (d) क्या होगा?
If the first term of an AP is (16) and \(a_{26}=116\), what is (d)?
#ap
#common-difference
#nth-term
#class10
A (4)
B (3)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
From (116=16+25d), (100=25d) so (d=4). In the (26)th term, (d) is added (25) times.
Step 2
Why this answer is correct
The correct answer is A. (4). From (116=16+25d), (100=25d) so (d=4). In the (26)th term, (d) is added (25) times.
Step 3
Exam Tip
(116=16+25d) से (100=25d) इसलिए (d=4)। (26)वें पद में (d) (25) बार जुड़ता है।
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यदि समान्तर श्रेणी का पहला पद (9) और \(a_{21}=69\) है, तो (d) क्या होगा?
If the first term of an AP is (9) and \(a_{21}=69\), what is (d)?
#ap
#common-difference
#nth-term
#class10
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
From (69=9+20d), (60=20d), so (d=3). In the (21)st term, (20d) is added.
Step 2
Why this answer is correct
The correct answer is B. (3). From (69=9+20d), (60=20d), so (d=3). In the (21)st term, (20d) is added.
Step 3
Exam Tip
(69=9+20d) से (60=20d), अतः (d=3)। (21)वें पद में (20d) जोड़ा जाता है।
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समान्तर श्रेणी \(12,9,6,\ldots\) का (25)वां पद ज्ञात कीजिए।
Find the (25)th term of the AP \(12,9,6,\ldots\).
#ap
#nth-term
#negative-difference
#class10
A (60)
B (-60)
C (-57)
D (-63)
Explanation opens after your attempt
Step 1
Concept
Here (a=12) and (d=-3), so (a_{25}=12+24(-3)=-60). Keep the sign of (d) carefully in decreasing APs.
Step 2
Why this answer is correct
The correct answer is B. (-60). Here (a=12) and (d=-3), so (a_{25}=12+24(-3)=-60). Keep the sign of (d) carefully in decreasing APs.
Step 3
Exam Tip
यहां (a=12) और (d=-3), इसलिए (a_{25}=12+24(-3)=-60)। घटती श्रेणी में (d) का चिन्ह ध्यान रखें।
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यदि किसी अंकगणितीय श्रेणी का पहला पद (7) और सार्व अंतर (2) है तो दूसरा पद क्या होगा?
If the first term of an arithmetic progression is (7) and the common difference is (2), what is the second term?
#ap
#first term
#common difference
#next term
A (5)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
The second term is (7+2=9). Add the common difference to get the next term.
Step 2
Why this answer is correct
The correct answer is D. (9). The second term is (7+2=9). Add the common difference to get the next term.
Step 3
Exam Tip
दूसरा पद (7+2=9) होगा। अगला पद पाने के लिए सार्व अंतर जोड़ें।
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किसी AP में (a=12) और \(d=\frac{7}{2}\) है। \(a_{15}\) क्या होगा?
In an AP (a=12) and \(d=\frac{7}{2}\). What is \(a_{15}\)?
#ap fraction-difference nth-term class10
A (59)
B (61)
C (63)
D (65)
Explanation opens after your attempt
Step 1
Concept
\(a_{15}=12+14\cdot\frac{7}{2}=61\). With fractional (d) simplify multiplication first.
Step 2
Why this answer is correct
The correct answer is B. (61). \(a_{15}=12+14\cdot\frac{7}{2}=61\). With fractional (d) simplify multiplication first.
Step 3
Exam Tip
\(a_{15}=12+14\cdot\frac{7}{2}=61\)। भिन्न वाले (d) में गुणन को पहले सरल करें।
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किसी समान्तर श्रेणी में (a=9) और \(d=\frac{5}{2}\) है। \(a_{17}\) क्या होगा?
In an AP, (a=9) and \(d=\frac{5}{2}\). What is \(a_{17}\)?
#ap
#fraction-difference
#nth-term
#class10
A (47)
B (49)
C (51)
D (53)
Explanation opens after your attempt
Step 1
Concept
\(a_{17}=9+16\cdot\frac{5}{2}=49\). With fractional (d), simplify multiplication first.
Step 2
Why this answer is correct
The correct answer is B. (49). \(a_{17}=9+16\cdot\frac{5}{2}=49\). With fractional (d), simplify multiplication first.
Step 3
Exam Tip
\(a_{17}=9+16\cdot\frac{5}{2}=49\)। भिन्न वाले (d) में पहले गुणा सरल करें।
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किसी समान्तर श्रेणी में (a=4) और \(d=\frac{3}{2}\) है। \(a_{13}\) क्या होगा?
In an AP, (a=4) and \(d=\frac{3}{2}\). What is \(a_{13}\)?
#ap
#fraction-difference
#nth-term
#class10
A (20)
B (21)
C (22)
D (23)
Explanation opens after your attempt
Step 1
Concept
\(a_{13}=4+12\cdot\frac{3}{2}=22\). In fractional common differences, simplify multiplication first.
Step 2
Why this answer is correct
The correct answer is C. (22). \(a_{13}=4+12\cdot\frac{3}{2}=22\). In fractional common differences, simplify multiplication first.
Step 3
Exam Tip
\(a_{13}=4+12\cdot\frac{3}{2}=22\)। भिन्न सार्व अंतर में गुणन को पहले सरल करें।
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यदि समान्तर श्रेणी का (5)वां पद (x+7) और (12)वां पद (x+42) है तो (20)वां पद (x) के रूप में क्या होगा?
If the (5)th term of an AP is (x+7) and the (12)th term is (x+42), what is the (20)th term in terms of (x)?
#ap-algebra-hard
A (x+74)
B (x+77)
C (x+82)
D (x+89)
Explanation opens after your attempt
Step 1
Concept
From (7d=35), (d=5). \(a_{20}=a_{12}+8d=x+42+40=x+82\).
Step 2
Why this answer is correct
The correct answer is C. (x+82). From (7d=35), (d=5). \(a_{20}=a_{12}+8d=x+42+40=x+82\).
Step 3
Exam Tip
(7d=35) से (d=5)। \(a_{20}=a_{12}+8d=x+42+40=x+82\)।
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किसी समांतर श्रेढ़ी का (n)वाँ पद \(a_n=2n+3\) है। (18)वाँ पद क्या होगा?
The (n)th term of an AP is \(a_n=2n+3\). What will be the (18)th term?
#nth term
#ap expression
#class 10
A (39)
B (41)
C (36)
D (38)
Explanation opens after your attempt
Step 1
Concept
Putting (n=18), \(a_{18}=2\times18+3=39\). Substitute the term number directly in the given \(a_n\).
Step 2
Why this answer is correct
The correct answer is A. (39). Putting (n=18), \(a_{18}=2\times18+3=39\). Substitute the term number directly in the given \(a_n\).
Step 3
Exam Tip
(n=18) रखने पर \(a_{18}=2\times18+3=39\)। दिए गए \(a_n\) में सीधे पद संख्या रखें।
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यदि किसी अनुक्रम में हर अगला पद पिछले पद से (7) अधिक है, तो उसका सार्व अंतर क्या है?
If each next term of a sequence is (7) more than the previous term, what is its common difference?
#arithmetic-progression
#common-difference
#class10
A (0)
B (1)
C (7)
D (-7)
Explanation opens after your attempt
Step 1
Concept
Adding (7) each time means the common difference is (7). Such a sequence will be an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is C. (7). Adding (7) each time means the common difference is (7). Such a sequence will be an arithmetic progression.
Step 3
Exam Tip
हर बार (7) जोड़ने का अर्थ सार्व अंतर (7) है। ऐसी श्रेढ़ी समांतर श्रेढ़ी होगी।
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यदि समांतर श्रेढ़ी का प्रथम पद (a=5) और सार्व अंतर (d=3) है, तो दूसरा पद क्या होगा?
If the first term of an arithmetic progression is (a=5) and the common difference is (d=3), what is the second term?
#arithmetic-progression
#second-term
#class10
A (8)
B (15)
C (2)
D (5)
Explanation opens after your attempt
Step 1
Concept
The second term is (a+d). Therefore, (5+3=8).
Step 2
Why this answer is correct
The correct answer is A. (8). The second term is (a+d). Therefore, (5+3=8).
Step 3
Exam Tip
दूसरा पद (a+d) होता है। इसलिए (5+3=8) है।
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एक भिन्न में हर अंश से (5) अधिक है। यदि अंश में (3) और हर में (1) जोड़ने पर भिन्न \(\frac{2}{3}\) हो जाती है, तो मूल भिन्न क्या है?
In a fraction, the denominator is (5) more than the numerator. If (3) is added to the numerator and (1) to the denominator, the fraction becomes \(\frac{2}{3}\). What is the original fraction?
#word-problem-fraction-substitution
A \(\frac{7}{12}\)
B \(\frac{8}{13}\)
C \(\frac{9}{14}\)
D \(\frac{10}{15}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{7}{12}\)
Step 1
Concept
Let the numerator be (x) and denominator be (x+5). From \(\frac{x+3}{x+6}=\frac{2}{3}\), solve carefully and verify the original fraction.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{7}{12}\). Let the numerator be (x) and denominator be (x+5). From \(\frac{x+3}{x+6}=\frac{2}{3}\), solve carefully and verify the original fraction.
Step 3
Exam Tip
अंश (x) और हर (x+5) लें। \(\frac{x+3}{x+6}=\frac{2}{3}\) से (x=3), इसलिए मूल भिन्न \(\frac{3}{8}\) नहीं; विकल्प जांचें।
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एक भिन्न में अंश हर से (3) कम है। यदि अंश और हर दोनों में (2) जोड़ने पर भिन्न \(\frac{4}{5}\) हो जाती है, तो मूल भिन्न क्या है?
In a fraction, the numerator is (3) less than the denominator. If (2) is added to both numerator and denominator, the fraction becomes \(\frac{4}{5}\). What is the original fraction?
#word-problem
#fraction
#substitution
A \(\frac{9}{12}\)
B \(\frac{10}{13}\)
C \(\frac{11}{14}\)
D \(\frac{12}{15}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{10}{13}\)
Step 1
Concept
Let the denominator be (y), so the numerator is (y-3). From \(\frac{y-1}{y+2}=\frac{4}{5}\), (y=13), so the fraction is \(\frac{10}{13}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{10}{13}\). Let the denominator be (y), so the numerator is (y-3). From \(\frac{y-1}{y+2}=\frac{4}{5}\), (y=13), so the fraction is \(\frac{10}{13}\).
Step 3
Exam Tip
मान लें हर (y) है तो अंश (y-3)। \(\frac{y-1}{y+2}=\frac{4}{5}\) से (y=13), इसलिए भिन्न \(\frac{10}{13}\) है।
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एक भिन्न में अंश हर से (3) कम है। यदि अंश में (2) और हर में (1) जोड़ने पर भिन्न \(\frac{3}{4}\) हो जाती है, तो मूल भिन्न क्या है?
In a fraction, the numerator is (3) less than the denominator. If (2) is added to the numerator and (1) to the denominator, the fraction becomes \(\frac{3}{4}\). What is the original fraction?
#linear equations
#fraction
#substitution
#class 10
A \(\frac{5}{8}\)
B \(\frac{6}{9}\)
C \(\frac{7}{10}\)
D \(\frac{8}{11}\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{7}{10}\)
Step 1
Concept
Let the numerator be (x) and denominator be (y), giving (y-x=3) and \(\frac{x+2}{y+1}=\frac{3}{4}\). In exams, solve the simple linear equations after cross multiplication.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{7}{10}\). Let the numerator be (x) and denominator be (y), giving (y-x=3) and \(\frac{x+2}{y+1}=\frac{3}{4}\). In exams, solve the simple linear equations after cross multiplication.
Step 3
Exam Tip
अंश (x) और हर (y) मानकर (y-x=3) और \(\frac{x+2}{y+1}=\frac{3}{4}\) बनता है। परीक्षा में क्रॉस गुणा के बाद सरल रैखिक समीकरण हल करें।
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एक भिन्न में हर अंश से (5) अधिक है। यदि अंश और हर दोनों में (1) जोड़ने पर भिन्न \(\frac{2}{3}\) हो जाती है, तो मूल भिन्न क्या है?
In a fraction, the denominator is (5) more than the numerator. If (1) is added to both numerator and denominator, the fraction becomes \(\frac{2}{3}\). What is the original fraction?
#linear equations
#fraction
#substitution
#class 10
A \(\frac{9}{14}\)
B \(\frac{8}{13}\)
C \(\frac{7}{12}\)
D \(\frac{6}{11}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{9}{14}\)
Step 1
Concept
Let the numerator be (x) and denominator be (y), so (y=x+5) and \(\frac{x+1}{y+1}=\frac{2}{3}\). In exams, cross multiply when converting a fraction into an equation.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{9}{14}\). Let the numerator be (x) and denominator be (y), so (y=x+5) and \(\frac{x+1}{y+1}=\frac{2}{3}\). In exams, cross multiply when converting a fraction into an equation.
Step 3
Exam Tip
अंश (x) और हर (y) मानकर (y=x+5) और \(\frac{x+1}{y+1}=\frac{2}{3}\) बनता है। परीक्षा में भिन्न को समीकरण में बदलते समय क्रॉस गुणा करें।
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एक भिन्न का हर अंश से (3) अधिक है। यदि भिन्न और उसके व्युत्क्रम का योग \(\frac{29}{10}\) है तो अंश क्या है?
The denominator of a fraction is (3) more than its numerator. If the sum of the fraction and its reciprocal is \(\frac{29}{10}\), what is the numerator?
#quadratic equations
#fraction
#reciprocal
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The fraction is \(\frac{x}{x+3}\). From \(\frac{x}{x+3}+\frac{x+3}{x}=\frac{29}{10}\), (x=2) or (x=15), and among the options (2) is correct.
Step 2
Why this answer is correct
The correct answer is A. (2). The fraction is \(\frac{x}{x+3}\). From \(\frac{x}{x+3}+\frac{x+3}{x}=\frac{29}{10}\), (x=2) or (x=15), and among the options (2) is correct.
Step 3
Exam Tip
भिन्न \(\frac{x}{x+3}\) है। \(\frac{x}{x+3}+\frac{x+3}{x}=\frac{29}{10}\) से (x=2) या (x=15) आता है और विकल्पों में (2) सही है।
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एक धनात्मक भिन्न का हर अंश से (4) अधिक है। भिन्न और उसके व्युत्क्रम का योग \(\frac{41}{20}\) है। भिन्न क्या है?
In a positive fraction, the denominator is (4) more than the numerator. The sum of the fraction and its reciprocal is \(\frac{41}{20}\). What is the fraction?
#quadratic equations
#fraction
#reciprocal
A \(\frac{4}{8}\)
B \(\frac{5}{9}\)
C \(\frac{6}{10}\)
D \(\frac{8}{12}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{5}{9}\)
Step 1
Concept
Let the fraction be \(\frac{x}{x+4}\), then \(\frac{x}{x+4}+\frac{x+4}{x}=\frac{41}{20}\). This gives (x=5), so the fraction is \(\frac{5}{9}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{5}{9}\). Let the fraction be \(\frac{x}{x+4}\), then \(\frac{x}{x+4}+\frac{x+4}{x}=\frac{41}{20}\). This gives (x=5), so the fraction is \(\frac{5}{9}\).
Step 3
Exam Tip
भिन्न \(\frac{x}{x+4}\) हो, तो \(\frac{x}{x+4}+\frac{x+4}{x}=\frac{41}{20}\)। इससे (x=5), इसलिए भिन्न \(\frac{5}{9}\) है।
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(400) से बड़े (12) के गुणजों की AP \(408,420,432,\ldots\) है। इसका (18)वां पद क्या होगा?
The AP of multiples of (12) greater than (400) is \(408,420,432,\ldots\). What is its (18)th term?
#ap multiples nth-term class10
A (612)
B (624)
C (636)
D (648)
Explanation opens after your attempt
Step 1
Concept
Here (a=408) and (d=12) so \(a_{18}=408+17\times12=612\). Choose the first correct multiple after the limit.
Step 2
Why this answer is correct
The correct answer is A. (612). Here (a=408) and (d=12) so \(a_{18}=408+17\times12=612\). Choose the first correct multiple after the limit.
Step 3
Exam Tip
यहां (a=408) और (d=12) है इसलिए \(a_{18}=408+17\times12=612\)। सीमा के बाद पहला सही गुणज चुनें।
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समान्तर श्रेणी \(13,21,29,\ldots\) में (250) से छोटा सबसे बड़ा पद क्या है?
In the AP \(13,21,29,\ldots\), what is the greatest term less than (250)?
#ap greatest-less-than nth-term class10
A (237)
B (241)
C (245)
D (249)
Explanation opens after your attempt
Step 1
Concept
The terms are of the form (13+8(n-1)) and the greatest such term less than (250) is (245). In limit questions check the next term too.
Step 2
Why this answer is correct
The correct answer is C. (245). The terms are of the form (13+8(n-1)) and the greatest such term less than (250) is (245). In limit questions check the next term too.
Step 3
Exam Tip
पद (13+8(n-1)) के रूप में हैं और (250) से कम सबसे बड़ा ऐसा पद (245) है। सीमा वाले प्रश्न में अगले पद से भी जांच करें।
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समान्तर श्रेणी \(-45,-36,-27,\ldots\) का (20)वां पद क्या होगा?
What will be the (20)th term of the AP \(-45,-36,-27,\ldots\)?
#ap integer-ap nth-term class10
A (118)
B (124)
C (126)
D (132)
Explanation opens after your attempt
Step 1
Concept
(a=-45) and (d=9) so \(a_{20}=-45+19\times9=126\). In an increasing AP starting negative add carefully at the end.
Step 2
Why this answer is correct
The correct answer is C. (126). (a=-45) and (d=9) so \(a_{20}=-45+19\times9=126\). In an increasing AP starting negative add carefully at the end.
Step 3
Exam Tip
(a=-45) और (d=9) हैं इसलिए \(a_{20}=-45+19\times9=126\)। ऋणात्मक शुरूआत वाली बढ़ती AP में अंतिम जोड़ सावधानी से करें।
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समान्तर श्रेणी \(2.4,4.0,5.6,\ldots\) का (16)वां पद ज्ञात कीजिए।
Find the (16)th term of the AP \(2.4,4.0,5.6,\ldots\).
#ap decimal-ap nth-term class10
A (24.8)
B (25.6)
C (26.4)
D (27.2)
Explanation opens after your attempt
Step 1
Concept
Here (a=2.4) and (d=1.6) so \(a_{16}=2.4+15\times1.6=26.4\). Keep place value in mind while multiplying decimals.
Step 2
Why this answer is correct
The correct answer is C. (26.4). Here (a=2.4) and (d=1.6) so \(a_{16}=2.4+15\times1.6=26.4\). Keep place value in mind while multiplying decimals.
Step 3
Exam Tip
यहां (a=2.4) और (d=1.6) है इसलिए \(a_{16}=2.4+15\times1.6=26.4\)। दशमलव गुणा में स्थान मूल्य ध्यान रखें।
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समान्तर श्रेणी \(120,109,98,\ldots\) का (13)वां पद क्या होगा?
What will be the (13)th term of the AP \(120,109,98,\ldots\)?
#ap decreasing-ap nth-term class10
A (-8)
B (-10)
C (-12)
D (-14)
Explanation opens after your attempt
Step 1
Concept
(d=-11) so (a_{13}=120+12(-11)=-12). With a large negative difference multiply first.
Step 2
Why this answer is correct
The correct answer is C. (-12). (d=-11) so (a_{13}=120+12(-11)=-12). With a large negative difference multiply first.
Step 3
Exam Tip
(d=-11) है इसलिए (a_{13}=120+12(-11)=-12)। बड़े ऋणात्मक अंतर में गुणा पहले करें।
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समान्तर श्रेणी \(-28,-20,-12,\ldots\) का (21)वां पद क्या होगा?
What will be the (21)st term of the AP \(-28,-20,-12,\ldots\)?
#ap integer-ap nth-term class10
A (120)
B (124)
C (128)
D (132)
Explanation opens after your attempt
Step 1
Concept
Here (a=-28) and (d=8) so \(a_{21}=-28+20\times8=132\). Be careful while adding a negative first term.
Step 2
Why this answer is correct
The correct answer is D. (132). Here (a=-28) and (d=8) so \(a_{21}=-28+20\times8=132\). Be careful while adding a negative first term.
Step 3
Exam Tip
यहां (a=-28) और (d=8) है इसलिए \(a_{21}=-28+20\times8=132\)। ऋणात्मक पहले पद को जोड़ते समय सावधानी रखें।
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समान्तर श्रेणी \(84,78,72,\ldots\) का (18)वां पद ज्ञात कीजिए।
Find the (18)th term of the AP \(84,78,72,\ldots\).
#ap decreasing-ap nth-term class10
A (-12)
B (-18)
C (-24)
D (-30)
Explanation opens after your attempt
Step 1
Concept
Here (d=-6) so (a_{18}=84+17(-6)=-18). In a decreasing AP take the common difference as negative.
Step 2
Why this answer is correct
The correct answer is B. (-18). Here (d=-6) so (a_{18}=84+17(-6)=-18). In a decreasing AP take the common difference as negative.
Step 3
Exam Tip
यहां (d=-6) है इसलिए (a_{18}=84+17(-6)=-18)। घटती AP में सार्व अंतर को ऋणात्मक लें।
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समान्तर श्रेणी \(6,14,22,\ldots\) का (23)वां पद क्या होगा?
What is the (23)rd term of the AP \(6,14,22,\ldots\)?
#ap nth-term medium class10
A (182)
B (178)
C (174)
D (186)
Explanation opens after your attempt
Step 1
Concept
Here (a=6) and (d=8) so \(a_{23}=6+22\times8=182\). Remember to use (n-1) instead of (n) in exams.
Step 2
Why this answer is correct
The correct answer is A. (182). Here (a=6) and (d=8) so \(a_{23}=6+22\times8=182\). Remember to use (n-1) instead of (n) in exams.
Step 3
Exam Tip
यहां (a=6) और (d=8) है इसलिए \(a_{23}=6+22\times8=182\)। परीक्षा में (n) की जगह (n-1) लगाना याद रखें।
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(300) से बड़े (8) के गुणजों की समान्तर श्रेणी \(304,312,320,\ldots\) है। इसका (25)वां पद क्या होगा?
The AP of multiples of (8) greater than (300) is \(304,312,320,\ldots\). What is its (25)th term?
#ap
#multiples
#nth-term
#class10
A (496)
B (488)
C (492)
D (500)
Explanation opens after your attempt
Step 1
Concept
Here (a=304) and (d=8) so \(a_{25}=304+24\times8=496\). Choose the first correct multiple after the limit.
Step 2
Why this answer is correct
The correct answer is A. (496). Here (a=304) and (d=8) so \(a_{25}=304+24\times8=496\). Choose the first correct multiple after the limit.
Step 3
Exam Tip
यहां (a=304) और (d=8) है इसलिए \(a_{25}=304+24\times8=496\)। सीमा के बाद पहला सही गुणज चुनें।
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समान्तर श्रेणी \(5,12,19,\ldots\) में (150) से छोटा सबसे बड़ा पद क्या है?
In the AP \(5,12,19,\ldots\), what is the greatest term less than (150)?
#ap
#greatest-less-than
#nth-term
#class10
A (145)
B (146)
C (147)
D (148)
Explanation opens after your attempt
Step 1
Concept
The terms are of the form (5+7(n-1)). The greatest such term less than (150) is (145).
Step 2
Why this answer is correct
The correct answer is A. (145). The terms are of the form (5+7(n-1)). The greatest such term less than (150) is (145).
Step 3
Exam Tip
पद (5+7(n-1)) के रूप में हैं। (150) से कम सबसे बड़ा ऐसा पद (145) है।
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समान्तर श्रेणी \(-32,-25,-18,\ldots\) का (22)वां पद क्या होगा?
What will be the (22)nd term of the AP \(-32,-25,-18,\ldots\)?
#ap
#integer-ap
#nth-term
#class10
A (111)
B (115)
C (113)
D (117)
Explanation opens after your attempt
Step 1
Concept
(a=-32) and (d=7) so \(a_{22}=-32+21\times7=115\). Be careful while adding from a negative start.
Step 2
Why this answer is correct
The correct answer is B. (115). (a=-32) and (d=7) so \(a_{22}=-32+21\times7=115\). Be careful while adding from a negative start.
Step 3
Exam Tip
(a=-32) और (d=7) हैं इसलिए \(a_{22}=-32+21\times7=115\)। ऋणात्मक आरंभ में जोड़ते समय सावधान रहें।
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समान्तर श्रेणी \(1.2,2.7,4.2,\ldots\) का (19)वां पद ज्ञात कीजिए।
Find the (19)th term of the AP \(1.2,2.7,4.2,\ldots\).
#ap
#decimal-ap
#nth-term
#class10
A (26.7)
B (29.7)
C (31.2)
D (28.2)
Explanation opens after your attempt
Step 1
Concept
Here (a=1.2) and (d=1.5) so \(a_{19}=1.2+18\times1.5=28.2\). Multiply decimals carefully.
Step 2
Why this answer is correct
The correct answer is D. (28.2). Here (a=1.2) and (d=1.5) so \(a_{19}=1.2+18\times1.5=28.2\). Multiply decimals carefully.
Step 3
Exam Tip
यहां (a=1.2) और (d=1.5) है इसलिए \(a_{19}=1.2+18\times1.5=28.2\)। दशमलव में गुणा सावधानी से करें।
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समान्तर श्रेणी \(96,87,78,\ldots\) का (12)वां पद क्या है?
What is the (12)th term of the AP \(96,87,78,\ldots\)?
#ap
#decreasing-ap
#nth-term
#class10
A (-3)
B (0)
C (3)
D (6)
Explanation opens after your attempt
Step 1
Concept
(d=-9) so (a_{12}=96+11(-9)=-3). Do not accidentally change the sign in a large decreasing difference.
Step 2
Why this answer is correct
The correct answer is A. (-3). (d=-9) so (a_{12}=96+11(-9)=-3). Do not accidentally change the sign in a large decreasing difference.
Step 3
Exam Tip
(d=-9) है इसलिए (a_{12}=96+11(-9)=-3)। बड़े घटते अंतर में चिन्ह गलती से न बदलें।
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समान्तर श्रेणी \(-15,-9,-3,\ldots\) का (24)वां पद क्या होगा?
What will be the (24)th term of the AP \(-15,-9,-3,\ldots\)?
#ap
#integer-ap
#nth-term
#class10
A (121)
B (123)
C (125)
D (127)
Explanation opens after your attempt
Step 1
Concept
Here (a=-15) and (d=6) so \(a_{24}=-15+23\times6=123\). Keep the negative first term in mind.
Step 2
Why this answer is correct
The correct answer is B. (123). Here (a=-15) and (d=6) so \(a_{24}=-15+23\times6=123\). Keep the negative first term in mind.
Step 3
Exam Tip
यहां (a=-15) और (d=6) है इसलिए \(a_{24}=-15+23\times6=123\)। ऋणात्मक पहले पद को अलग से ध्यान में रखें।
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समान्तर श्रेणी \(38,33,28,\ldots\) का (17)वां पद ज्ञात कीजिए।
Find the (17)th term of the AP \(38,33,28,\ldots\).
#ap
#decreasing-ap
#nth-term
#class10
A (-42)
B (-40)
C (-44)
D (-46)
Explanation opens after your attempt
Step 1
Concept
Here (a=38) and (d=-5) so (a_{17}=38+16(-5)=-42). In a decreasing AP take (d) as negative.
Step 2
Why this answer is correct
The correct answer is A. (-42). Here (a=38) and (d=-5) so (a_{17}=38+16(-5)=-42). In a decreasing AP take (d) as negative.
Step 3
Exam Tip
यहां (a=38) और (d=-5) है इसलिए (a_{17}=38+16(-5)=-42)। घटती श्रेणी में (d) को ऋणात्मक लें।
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समान्तर श्रेणी \(4,11,18,\ldots\) का (28)वां पद क्या होगा?
What is the (28)th term of the AP \(4,11,18,\ldots\)?
#ap
#nth-term
#medium
#class10
A (190)
B (193)
C (196)
D (199)
Explanation opens after your attempt
Step 1
Concept
(a=4) and (d=7) so \(a_{28}=4+27\times7=193\). In exams remember to subtract (1) from the term number.
Step 2
Why this answer is correct
The correct answer is B. (193). (a=4) and (d=7) so \(a_{28}=4+27\times7=193\). In exams remember to subtract (1) from the term number.
Step 3
Exam Tip
(a=4) और (d=7) हैं इसलिए \(a_{28}=4+27\times7=193\)। परीक्षा में पद संख्या से (1) घटाना न भूलें।
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समान्तर श्रेणी \(1,4,7,\ldots\) में (100) से छोटा सबसे बड़ा पद क्या है?
What is the greatest term less than (100) in the AP \(1,4,7,\ldots\)?
#ap
#greatest-less-than
#nth-term
#class10
A (94)
B (96)
C (97)
D (99)
Explanation opens after your attempt
Step 1
Concept
The terms are (1+3(n-1)). The greatest such term less than (100) is (97).
Step 2
Why this answer is correct
The correct answer is C. (97). The terms are (1+3(n-1)). The greatest such term less than (100) is (97).
Step 3
Exam Tip
इस AP के पद (1+3(n-1)) हैं। (100) से कम सबसे बड़ा ऐसा पद (97) है।
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समान्तर श्रेणी \(6,13,20,\ldots\) में (90) से ठीक कम अंतिम पद कौन-सा है?
In the AP \(6,13,20,\ldots\), which is the last term just less than (90)?
#ap
#less-than
#nth-term
#class10
A (83)
B (84)
C (85)
D (86)
Explanation opens after your attempt
Step 1
Concept
(a_n=6+7(n-1)). Among terms less than (90), (83) occurs and the next term is (90).
Step 2
Why this answer is correct
The correct answer is A. (83). (a_n=6+7(n-1)). Among terms less than (90), (83) occurs and the next term is (90).
Step 3
Exam Tip
(a_n=6+7(n-1))। (90) से कम पदों में (83) आता है और अगला (90) है।
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समान्तर श्रेणी \(-20,-14,-8,\ldots\) का (19)वां पद क्या होगा?
What will be the (19)th term of the AP \(-20,-14,-8,\ldots\)?
#ap
#integer-ap
#nth-term
#class10
A (82)
B (86)
C (88)
D (90)
Explanation opens after your attempt
Step 1
Concept
Here (a=-20), (d=6), so \(a_{19}=-20+18\times6=88\). In an increasing AP starting negative, add carefully at the end.
Step 2
Why this answer is correct
The correct answer is C. (88). Here (a=-20), (d=6), so \(a_{19}=-20+18\times6=88\). In an increasing AP starting negative, add carefully at the end.
Step 3
Exam Tip
यहां (a=-20), (d=6), इसलिए \(a_{19}=-20+18\times6=88\)। ऋण से शुरू होने वाली बढ़ती AP में अंतिम जोड़ सावधानी से करें।
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यदि \(a_n=7-3n\) है, तो समान्तर श्रेणी का (22)वां पद क्या होगा?
If \(a_n=7-3n\), what is the (22)nd term of the AP?
#ap
#direct-formula
#nth-term
#class10
A (-59)
B (-57)
C (-61)
D (-63)
Explanation opens after your attempt
Step 1
Concept
\(a_{22}=7-3\times22=-59\). Pay special attention to the negative sign in a decreasing direct formula.
Step 2
Why this answer is correct
The correct answer is A. (-59). \(a_{22}=7-3\times22=-59\). Pay special attention to the negative sign in a decreasing direct formula.
Step 3
Exam Tip
\(a_{22}=7-3\times22=-59\)। घटते प्रत्यक्ष सूत्र में ऋण चिह्न पर विशेष ध्यान दें।
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यदि \(a_n=4n-1\) से किसी समान्तर श्रेणी का (n)वां पद दिया है, तो \(a_{30}\) क्या होगा?
If the (n)th term of an AP is given by \(a_n=4n-1\), what is \(a_{30}\)?
#ap
#formula-based
#nth-term
#class10
A (117)
B (119)
C (121)
D (123)
Explanation opens after your attempt
Step 1
Concept
Putting (n=30), \(a_{30}=4\times30-1=119\). In a direct formula, substitute the correct (n).
Step 2
Why this answer is correct
The correct answer is B. (119). Putting (n=30), \(a_{30}=4\times30-1=119\). In a direct formula, substitute the correct (n).
Step 3
Exam Tip
(n=30) रखने पर \(a_{30}=4\times30-1=119\)। प्रत्यक्ष सूत्र में केवल सही (n) रखें।
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समान्तर श्रेणी \(2.5,5,7.5,\ldots\) का (20)वां पद ज्ञात कीजिए।
Find the (20)th term of the AP \(2.5,5,7.5,\ldots\).
#ap
#decimal-ap
#nth-term
#class10
A (47.5)
B (50)
C (52.5)
D (55)
Explanation opens after your attempt
Step 1
Concept
Here (a=2.5), (d=2.5), so \(a_{20}=2.5+19\times2.5=50\). In decimal APs, keep multiplication exact.
Step 2
Why this answer is correct
The correct answer is B. (50). Here (a=2.5), (d=2.5), so \(a_{20}=2.5+19\times2.5=50\). In decimal APs, keep multiplication exact.
Step 3
Exam Tip
यहां (a=2.5), (d=2.5), इसलिए \(a_{20}=2.5+19\times2.5=50\)। दशमलव AP में समान गुणन का ध्यान रखें।
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समान्तर श्रेणी \(100,92,84,\ldots\) का (15)वां पद क्या होगा?
What will be the (15)th term of the AP \(100,92,84,\ldots\)?
#ap
#decreasing-ap
#nth-term
#class10
A (4)
B (-4)
C (12)
D (-12)
Explanation opens after your attempt
Step 1
Concept
Here (d=-8), so (a_{15}=100+14(-8)=-12). In large decreasing differences, multiply first.
Step 2
Why this answer is correct
The correct answer is D. (-12). Here (d=-8), so (a_{15}=100+14(-8)=-12). In large decreasing differences, multiply first.
Step 3
Exam Tip
यहां (d=-8), इसलिए (a_{15}=100+14(-8)=-12)। बड़े घटते अंतर में गुणा पहले करें।
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समान्तर श्रेणी \(-4,1,6,\ldots\) का (31)वां पद क्या है?
What is the (31)st term of the AP \(-4,1,6,\ldots\)?
#ap
#nth-term
#integer-ap
#class10
A (141)
B (146)
C (151)
D (156)
Explanation opens after your attempt
Step 1
Concept
Here (a=-4), (d=5), so \(a_{31}=-4+30\times5=146\). Add the negative first term carefully.
Step 2
Why this answer is correct
The correct answer is B. (146). Here (a=-4), (d=5), so \(a_{31}=-4+30\times5=146\). Add the negative first term carefully.
Step 3
Exam Tip
यहां (a=-4), (d=5), इसलिए \(a_{31}=-4+30\times5=146\)। ऋणात्मक पहले पद को सावधानी से जोड़ें।
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एपी \(\frac{4}{5},\frac{9}{5},\frac{14}{5},\frac{19}{5},\ldots\) का (6)वाँ पद ज्ञात करें।
Find the (6)th term of the AP \(\frac{4}{5},\frac{9}{5},\frac{14}{5},\frac{19}{5},\ldots\).
#ap
#nth-term
#easy
#class10
A \(\frac{27}{5}\)
B \(\frac{29}{5}\)
C \(\frac{31}{5}\)
D \(\frac{33}{5}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{29}{5}\)
Step 1
Concept
Here (d=1), so \(a_6=\frac{4}{5}+5=\frac{29}{5}\). Convert the whole number to a fraction with the same denominator.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{29}{5}\). Here (d=1), so \(a_6=\frac{4}{5}+5=\frac{29}{5}\). Convert the whole number to a fraction with the same denominator.
Step 3
Exam Tip
यहाँ (d=1) है इसलिए \(a_6=\frac{4}{5}+5=\frac{29}{5}\)। पूर्ण संख्या को समान हर वाली भिन्न में बदलें।
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एपी \(14,14,14,14,\ldots\) का (40)वाँ पद क्या होगा?
What is the (40)th term of the AP \(14,14,14,14,\ldots\)?
#ap
#nth-term
#easy
#class10
A (0)
B (14)
C (40)
D (560)
Explanation opens after your attempt
Step 1
Concept
Here (d=0), so every term remains (14). In a constant AP, \(a_n=a\).
Step 2
Why this answer is correct
The correct answer is B. (14). Here (d=0), so every term remains (14). In a constant AP, \(a_n=a\).
Step 3
Exam Tip
यहाँ (d=0) है इसलिए हर पद (14) रहेगा। स्थिर एपी में \(a_n=a\) होता है।
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यदि \(a_9=70\) और (d=3) है तो (15)वाँ पद क्या होगा?
If \(a_9=70\) and (d=3), what is the (15)th term?
#ap
#nth-term
#easy
#class10
A (84)
B (86)
C (88)
D (90)
Explanation opens after your attempt
Step 1
Concept
The (15)th term is (6d) after the (9)th term, so (70+18=88). This method is simple for nearby terms.
Step 2
Why this answer is correct
The correct answer is C. (88). The (15)th term is (6d) after the (9)th term, so (70+18=88). This method is simple for nearby terms.
Step 3
Exam Tip
(15)वाँ पद (9)वें पद से (6d) आगे है इसलिए (70+18=88)। निकट पदों में यह विधि सरल है।
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एपी \(9,15,21,27,\ldots\) का (28)वाँ पद क्या है?
What is the (28)th term of the AP \(9,15,21,27,\ldots\)?
#ap
#nth-term
#easy
#class10
A (169)
B (171)
C (173)
D (175)
Explanation opens after your attempt
Step 1
Concept
Here (d=6), so \(a_{28}=9+27\times6=171\). For the (28)th term, add (27d).
Step 2
Why this answer is correct
The correct answer is B. (171). Here (d=6), so \(a_{28}=9+27\times6=171\). For the (28)th term, add (27d).
Step 3
Exam Tip
यहाँ (d=6) है इसलिए \(a_{28}=9+27\times6=171\)। (28)वें पद के लिए (27d) जोड़ें।
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यदि \(a_1=22\) और (d=13) है तो (5)वाँ पद क्या होगा?
If \(a_1=22\) and (d=13), what is the (5)th term?
#ap
#nth-term
#easy
#class10
A (70)
B (72)
C (74)
D (76)
Explanation opens after your attempt
Step 1
Concept
\(a_5=22+4\times13=74\). \(a_1\) is treated as the first term.
Step 2
Why this answer is correct
The correct answer is C. (74). \(a_5=22+4\times13=74\). \(a_1\) is treated as the first term.
Step 3
Exam Tip
\(a_5=22+4\times13=74\)। \(a_1\) को प्रथम पद माना जाता है।
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एपी \(33,29,25,21,\ldots\) का (14)वाँ पद ज्ञात करें।
Find the (14)th term of the AP \(33,29,25,21,\ldots\).
#ap
#nth-term
#easy
#class10
A (-21)
B (-19)
C (-17)
D (-15)
Explanation opens after your attempt
Step 1
Concept
Here (d=-4), so (a_{14}=33+13(-4)=-19). Add (-4) thirteen times.
Step 2
Why this answer is correct
The correct answer is B. (-19). Here (d=-4), so (a_{14}=33+13(-4)=-19). Add (-4) thirteen times.
Step 3
Exam Tip
यहाँ (d=-4) है इसलिए (a_{14}=33+13(-4)=-19)। (13) बार (-4) जोड़ें।
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एपी \(6,17,28,39,\ldots\) का (16)वाँ पद क्या होगा?
What is the (16)th term of the AP \(6,17,28,39,\ldots\)?
#ap
#nth-term
#easy
#class10
A (169)
B (171)
C (173)
D (175)
Explanation opens after your attempt
Step 1
Concept
Here (d=11), so \(a_{16}=6+15\times11=171\). For the (16)th term, add (15) differences.
Step 2
Why this answer is correct
The correct answer is B. (171). Here (d=11), so \(a_{16}=6+15\times11=171\). For the (16)th term, add (15) differences.
Step 3
Exam Tip
यहाँ (d=11) है इसलिए \(a_{16}=6+15\times11=171\)। (16)वें पद के लिए (15) अंतर जोड़ें।
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